PetscErrorCode SNESDiffParameterCreate_More(SNES snes,Vec x,void **outneP)
{
DIFFPAR_MORE *neP;
Vec w;
PetscRandom rctx; /* random number generator context */
PetscErrorCode ierr;
PetscBool flg;
char noise_file[PETSC_MAX_PATH_LEN];
PetscFunctionBegin;
ierr = PetscNewLog(snes,DIFFPAR_MORE,&neP);CHKERRQ(ierr);
neP->function_count = 0;
neP->fnoise_min = 1.0e-20;
neP->hopt_min = 1.0e-8;
neP->h_first_try = 1.0e-3;
neP->fnoise_resets = 0;
neP->hopt_resets = 0;
/* Create work vectors */
ierr = VecDuplicateVecs(x,3,&neP->workv);CHKERRQ(ierr);
w = neP->workv[0];
/* Set components of vector w to random numbers */
ierr = PetscRandomCreate(((PetscObject)snes)->comm,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(w,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
/* Open output file */
ierr = PetscOptionsGetString(((PetscObject)snes)->prefix,"-snes_mf_noise_file",noise_file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (flg) neP->fp = fopen(noise_file,"w");
else neP->fp = fopen("noise.out","w");
if (!neP->fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_OPEN,"Cannot open file");
ierr = PetscInfo(snes,"Creating Jorge's differencing parameter context\n");CHKERRQ(ierr);
*outneP = neP;
PetscFunctionReturn(0);
}
Ensure(FFT, i_transform_is_inverse_of_transform)
{
Vec v;
PetscInt dim = 5;
DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,dim,2,1,NULL,&da);
DMCreateGlobalVector(da, &v);
PetscRandom rdm;
PetscRandomCreate(PETSC_COMM_WORLD, &rdm);
PetscRandomSetFromOptions(rdm);
VecSetRandom(v, rdm);
PetscRandomDestroy(&rdm);
Vec vIn;
VecDuplicate(v, &vIn);
VecCopy(v, vIn);
scFftCreate(da, &fft);
Vec x, y, z;
scFftCreateVecsFFTW(fft, &x, &y, &z);
int component = 0;
scFftTransform(fft, v, component, y);
scFftITransform(fft, v, component, y);
VecAXPY(v, -dim, vIn);
PetscReal error;
VecStrideNorm(v, component, NORM_INFINITY, &error);
assert_that(error < 1.0e-6, is_true);
VecDestroy(&x);
VecDestroy(&y);
VecDestroy(&z);
VecDestroy(&v);
VecDestroy(&vIn);
scFftDestroy(&fft);
DMDestroy(&da);
}
/*@
BVSetRandomColumn - Set one column of a BV to random numbers.
Logically Collective on BV
Input Parameters:
+ bv - basis vectors
. j - column number to be set
- rctx - the random number context, formed by PetscRandomCreate(), or NULL and
it will create one internally.
Note:
This operation is analogue to VecSetRandom - the difference is that the
generated random vector is the same irrespective of the size of the
communicator (if all processes pass a PetscRandom context initialized
with the same seed).
Level: advanced
.seealso: BVSetRandom(), BVSetActiveColumns()
@*/
PetscErrorCode BVSetRandomColumn(BV bv,PetscInt j,PetscRandom rctx)
{
PetscErrorCode ierr;
PetscRandom rand=NULL;
PetscInt i,low,high;
PetscScalar *px,t;
Vec x;
PetscFunctionBegin;
PetscValidHeaderSpecific(bv,BV_CLASSID,1);
PetscValidLogicalCollectiveInt(bv,j,2);
if (rctx) PetscValidHeaderSpecific(rctx,PETSC_RANDOM_CLASSID,3);
else {
ierr = PetscRandomCreate(PetscObjectComm((PetscObject)bv),&rand);CHKERRQ(ierr);
ierr = PetscRandomSetSeed(rand,0x12345678);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
rctx = rand;
}
PetscValidType(bv,1);
BVCheckSizes(bv,1);
if (j<0 || j>=bv->m) SETERRQ2(PetscObjectComm((PetscObject)bv),PETSC_ERR_ARG_OUTOFRANGE,"Argument j has wrong value %D, the number of columns is %D",j,bv->m);
ierr = PetscLogEventBegin(BV_SetRandom,bv,rctx,0,0);CHKERRQ(ierr);
ierr = BVGetColumn(bv,j,&x);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(x,&low,&high);CHKERRQ(ierr);
ierr = VecGetArray(x,&px);CHKERRQ(ierr);
for (i=0;i<bv->N;i++) {
ierr = PetscRandomGetValue(rctx,&t);CHKERRQ(ierr);
if (i>=low && i<high) px[i-low] = t;
}
ierr = VecRestoreArray(x,&px);CHKERRQ(ierr);
ierr = BVRestoreColumn(bv,j,&x);CHKERRQ(ierr);
ierr = PetscLogEventEnd(BV_SetRandom,bv,rctx,0,0);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscObjectStateIncrease((PetscObject)bv);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
BVSetRandom - Set the columns of a BV to random numbers.
Logically Collective on BV
Input Parameters:
+ bv - basis vectors
- rctx - the random number context, formed by PetscRandomCreate(), or NULL and
it will create one internally.
Note:
All active columns (except the leading ones) are modified.
Level: advanced
.seealso: BVSetRandomColumn(), BVSetActiveColumns()
@*/
PetscErrorCode BVSetRandom(BV bv,PetscRandom rctx)
{
PetscErrorCode ierr;
PetscRandom rand=NULL;
PetscInt i,low,high,k;
PetscScalar *px,t;
Vec x;
PetscFunctionBegin;
PetscValidHeaderSpecific(bv,BV_CLASSID,1);
if (rctx) PetscValidHeaderSpecific(rctx,PETSC_RANDOM_CLASSID,2);
else {
ierr = PetscRandomCreate(PetscObjectComm((PetscObject)bv),&rand);CHKERRQ(ierr);
ierr = PetscRandomSetSeed(rand,0x12345678);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
rctx = rand;
}
PetscValidType(bv,1);
BVCheckSizes(bv,1);
ierr = PetscLogEventBegin(BV_SetRandom,bv,rctx,0,0);CHKERRQ(ierr);
for (k=bv->l;k<bv->k;k++) {
ierr = BVGetColumn(bv,k,&x);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(x,&low,&high);CHKERRQ(ierr);
ierr = VecGetArray(x,&px);CHKERRQ(ierr);
for (i=0;i<bv->N;i++) {
ierr = PetscRandomGetValue(rctx,&t);CHKERRQ(ierr);
if (i>=low && i<high) px[i-low] = t;
}
ierr = VecRestoreArray(x,&px);CHKERRQ(ierr);
ierr = BVRestoreColumn(bv,k,&x);CHKERRQ(ierr);
}
ierr = PetscLogEventEnd(BV_SetRandom,bv,rctx,0,0);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscObjectStateIncrease((PetscObject)bv);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
Vec x,y,ys;
PetscTruth flg,disp_mat=PETSC_FALSE,disp_vec=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt m,i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0,norm;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_vec", &disp_vec);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
if (use_random){
ierr = VecSetRandom(x,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(x,1.0);CHKERRQ(ierr);
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&ys);CHKERRQ(ierr);
/* Test MatMult */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMult(As,x,ys);CHKERRQ(ierr);
if (disp_vec){
printf("y = A*x:\n");
ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"ys = As*x:\n");
ierr = VecView(ys,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecAXPY(y,-1.0,ys);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_INFINITY,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 || disp_vec){
printf("|| A*x - As*x || = %G\n",norm);
}
/* Free spaces */
if (use_random) {ierr = PetscRandomDestroy(rctx);CHKERRQ(ierr);}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(As);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(y);CHKERRQ(ierr);
ierr = VecDestroy(ys);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
typedef enum {RANDOM, CONSTANT, TANH, NUM_FUNCS} FuncType;
const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
PetscMPIInt size;
PetscInt n = 10,N,Ny,ndim=4,dim[4],DIM,i;
Vec x,y,z;
PetscScalar s;
PetscRandom rdm;
PetscReal enorm;
PetscInt func=RANDOM;
FuncType function = RANDOM;
PetscBool view = PETSC_FALSE;
PetscErrorCode ierr;
PetscScalar *x_array,*y_array,*z_array;
fftw_plan fplan,bplan;
const ptrdiff_t N0 = 20, N1 = 20;
ptrdiff_t alloc_local, local_n0, local_0_start;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires real numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
alloc_local=fftw_mpi_local_size_2d(N0, N1, PETSC_COMM_WORLD,
&local_n0, &local_0_start);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uniprocessor example only!");
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, PETSC_NULL, "FFTW Options", "ex142");CHKERRQ(ierr);
ierr = PetscOptionsEList("-function", "Function type", "ex142", funcNames, NUM_FUNCS, funcNames[function], &func, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the functions", "ex112", view, &view, PETSC_NULL);CHKERRQ(ierr);
function = (FuncType) func;
ierr = PetscOptionsEnd();CHKERRQ(ierr);
for (DIM = 0; DIM < ndim; DIM++){
dim[DIM] = n; /* size of real space vector in DIM-dimension */
}
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
for (DIM = 1; DIM < 5; DIM++){
/* create vectors of length N=dim[0]*dim[1]* ...*dim[DIM-1] */
/*----------------------------------------------------------*/
N = Ny = 1;
for (i = 0; i < DIM-1; i++) {
N *= dim[i];
}
Ny = N; Ny *= 2*(dim[DIM-1]/2 + 1); /* add padding elements to output vector y */
N *= dim[DIM-1];
ierr = PetscPrintf(PETSC_COMM_SELF, "\n %d-D: FFTW on vector of size %d \n",DIM,N);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,Ny,&y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = VecDuplicate(x,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* Set fftw plan */
/*----------------------------------*/
ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
ierr = VecGetArray(z,&z_array);CHKERRQ(ierr);
unsigned int flags = FFTW_ESTIMATE; //or FFTW_MEASURE
/* The data in the in/out arrays is overwritten during FFTW_MEASURE planning, so such planning
should be done before the input is initialized by the user. */
printf("DIM: %d, N %d, Ny %d\n",DIM,N,Ny);
switch (DIM){
case 1:
fplan = fftw_plan_dft_r2c_1d(dim[0], (double *)x_array, (fftw_complex*)y_array, flags);
bplan = fftw_plan_dft_c2r_1d(dim[0], (fftw_complex*)y_array, (double *)z_array, flags);
break;
case 2:
fplan = fftw_plan_dft_r2c_2d(dim[0],dim[1],(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r_2d(dim[0],dim[1],(fftw_complex*)y_array,(double *)z_array,flags);
break;
case 3:
fplan = fftw_plan_dft_r2c_3d(dim[0],dim[1],dim[2],(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r_3d(dim[0],dim[1],dim[2],(fftw_complex*)y_array,(double *)z_array,flags);
break;
default:
fplan = fftw_plan_dft_r2c(DIM,dim,(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r(DIM,dim,(fftw_complex*)y_array,(double *)z_array,flags);
break;
}
ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
ierr = VecRestoreArray(z,&z_array);CHKERRQ(ierr);
/* Initialize Real space vector x:
The data in the in/out arrays is overwritten during FFTW_MEASURE planning, so planning
should be done before the input is initialized by the user.
--------------------------------------------------------*/
if (function == RANDOM) {
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
} else if (function == CONSTANT) {
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
} else if (function == TANH) {
ierr = VecGetArray(x, &x_array);CHKERRQ(ierr);
for (i = 0; i < N; ++i) {
x_array[i] = tanh((i - N/2.0)*(10.0/N));
}
ierr = VecRestoreArray(x, &x_array);CHKERRQ(ierr);
}
if (view) {
ierr = VecView(x, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* FFT - also test repeated transformation */
/*-------------------------------------------*/
ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
ierr = VecGetArray(z,&z_array);CHKERRQ(ierr);
for (i=0; i<3; i++){
/* FFTW_FORWARD */
fftw_execute(fplan);
//printf("\n fout:\n");
//fftw_complex* fout = (fftw_complex*)y_array;
//for (i=0; i<N/2+1; i++) printf("%d (%g %g)\n",i,fout[i][0],fout[i][1]);
/* FFTW_BACKWARD: destroys its input array 'y_array' even for out-of-place transforms! */
fftw_execute(bplan);
}
ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
ierr = VecRestoreArray(z,&z_array);CHKERRQ(ierr);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
/*------------------------------------------------------------------*/
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view) {ierr = VecView(x, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
if (view) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %G\n",enorm);CHKERRQ(ierr);
}
/* free spaces */
fftw_destroy_plan(fplan);
fftw_destroy_plan(bplan);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode TestTriangle(MPI_Comm comm, PetscBool interpolate, PetscBool transform)
{
DM dm;
PetscRandom r, ang, ang2;
PetscInt dim, t;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Create reference triangle */
dim = 2;
ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) dm, "triangle");CHKERRQ(ierr);
ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
ierr = DMPlexSetDimension(dm, dim);CHKERRQ(ierr);
{
PetscInt numPoints[2] = {3, 1};
PetscInt coneSize[4] = {3, 0, 0, 0};
PetscInt cones[3] = {1, 2, 3};
PetscInt coneOrientations[3] = {0, 0, 0};
PetscScalar vertexCoords[6] = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0};
ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
if (interpolate) {
DM idm;
ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) idm, "triangle");CHKERRQ(ierr);
ierr = DMPlexCopyCoordinates(dm, idm);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
dm = idm;
}
ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
}
/* Check reference geometry: determinant is scaled by reference volume (2.0) */
{
PetscReal v0Ex[2] = {-1.0, -1.0};
PetscReal JEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal invJEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[2] = {-0.333333333333, -0.333333333333};
PetscReal normalEx[2] = {0.0, 0.0};
PetscReal volEx = 2.0;
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Check random triangles: rotate, scale, then translate */
if (transform) {
ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(r, 0.0, 10.0);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang, 0.0, 2*PETSC_PI);CHKERRQ(ierr);
for (t = 0; t < 100; ++t) {
PetscScalar vertexCoords[6] = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0}, trans[2];
PetscReal v0Ex[2] = {-1.0, -1.0};
PetscReal JEx[4] = {1.0, 0.0, 0.0, 1.0}, R[4], rot[2], rotM[4];
PetscReal invJEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0, scale, phi;
PetscReal centroidEx[2] = {-0.333333333333, -0.333333333333};
PetscReal normalEx[2] = {0.0, 0.0};
PetscReal volEx = 2.0;
PetscInt d, e, f, p;
ierr = PetscRandomGetValueReal(r, &scale);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang, &phi);CHKERRQ(ierr);
R[0] = cos(phi); R[1] = -sin(phi);
R[2] = sin(phi); R[3] = cos(phi);
for (p = 0; p < 3; ++p) {
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * vertexCoords[p*dim+e];
}
}
for (d = 0; d < dim; ++d) vertexCoords[p*dim+d] = rot[d];
}
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * centroidEx[e];
}
}
for (d = 0; d < dim; ++d) centroidEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += R[d*dim+f] * JEx[f*dim+e];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += invJEx[d*dim+f] * R[e*dim+f];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
invJEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
ierr = PetscRandomGetValueReal(r, &trans[d]);CHKERRQ(ierr);
for (p = 0; p < 3; ++p) {
vertexCoords[p*dim+d] *= scale;
vertexCoords[p*dim+d] += trans[d];
}
v0Ex[d] = vertexCoords[d];
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] *= scale;
invJEx[d*dim+e] /= scale;
}
detJEx *= scale;
centroidEx[d] *= scale;
centroidEx[d] += trans[d];
volEx *= scale;
}
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang);CHKERRQ(ierr);
}
/* Move to 3D: Check reference geometry: determinant is scaled by reference volume (2.0) */
dim = 3;
{
PetscScalar vertexCoords[9] = {-1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0, 0.0};
PetscReal v0Ex[3] = {-1.0, -1.0, 0.0};
PetscReal JEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal invJEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[3] = {-0.333333333333, -0.333333333333, 0.0};
PetscReal normalEx[3] = {0.0, 0.0, 1.0};
PetscReal volEx = 2.0;
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Rotated reference element */
{
PetscScalar vertexCoords[9] = {0.0, -1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0};
PetscReal v0Ex[3] = {0.0, -1.0, -1.0};
PetscReal JEx[9] = {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0};
PetscReal invJEx[9] = {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[3] = {0.0, -0.333333333333, -0.333333333333};
PetscReal normalEx[3] = {1.0, 0.0, 0.0};
PetscReal volEx = 2.0;
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Check random triangles: scale, translate, then rotate */
if (transform) {
ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(r, 0.0, 10.0);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang, 0.0, 2*PETSC_PI);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang2);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang2);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang2, 0.0, PETSC_PI);CHKERRQ(ierr);
for (t = 0; t < 100; ++t) {
PetscScalar vertexCoords[9] = {-1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0, 0.0}, trans[3];
PetscReal v0Ex[3] = {-1.0, -1.0, 0.0};
PetscReal JEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0}, R[9], rot[3], rotM[9];
PetscReal invJEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0, scale, phi, theta, psi = 0.0;
PetscReal centroidEx[3] = {-0.333333333333, -0.333333333333, 0.0};
PetscReal normalEx[3] = {0.0, 0.0, 1.0};
PetscReal volEx = 2.0;
PetscInt d, e, f, p;
ierr = PetscRandomGetValueReal(r, &scale);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang, &phi);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang2, &theta);CHKERRQ(ierr);
for (d = 0; d < dim; ++d) {
ierr = PetscRandomGetValueReal(r, &trans[d]);CHKERRQ(ierr);
for (p = 0; p < 3; ++p) {
vertexCoords[p*dim+d] *= scale;
vertexCoords[p*dim+d] += trans[d];
}
centroidEx[d] *= scale;
centroidEx[d] += trans[d];
for (e = 0; e < dim-1; ++e) {
JEx[d*dim+e] *= scale;
invJEx[d*dim+e] /= scale;
}
if (d < dim-1) {
detJEx *= scale;
volEx *= scale;
}
}
R[0] = cos(theta)*cos(psi); R[1] = sin(phi)*sin(theta)*cos(psi) - cos(phi)*sin(psi); R[2] = sin(phi)*sin(psi) + cos(phi)*sin(theta)*cos(psi);
R[3] = cos(theta)*sin(psi); R[4] = cos(phi)*cos(psi) + sin(phi)*sin(theta)*sin(psi); R[5] = cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi);
R[6] = -sin(theta); R[7] = sin(phi)*cos(theta); R[8] = cos(phi)*cos(theta);
for (p = 0; p < 3; ++p) {
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * vertexCoords[p*dim+e];
}
}
for (d = 0; d < dim; ++d) vertexCoords[p*dim+d] = rot[d];
}
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * centroidEx[e];
}
}
for (d = 0; d < dim; ++d) centroidEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * normalEx[e];
}
}
for (d = 0; d < dim; ++d) normalEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
v0Ex[d] = vertexCoords[d];
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += R[d*dim+f] * JEx[f*dim+e];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += invJEx[d*dim+f] * R[e*dim+f];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
invJEx[d*dim+e] = rotM[d*dim+e];
}
}
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang2);CHKERRQ(ierr);
}
/* Cleanup */
ierr = DMDestroy(&dm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* KSP context */
PetscErrorCode ierr;
PetscInt n = 10,its, dim,p = 1,use_random;
PetscScalar none = -1.0,pfive = 0.5;
PetscReal norm;
PetscRandom rctx;
TestType type;
PetscBool flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-p",&p,PETSC_NULL);CHKERRQ(ierr);
switch (p) {
case 1: type = TEST_1; dim = n; break;
case 2: type = TEST_2; dim = n; break;
case 3: type = TEST_3; dim = n; break;
case 4: type = HELMHOLTZ_1; dim = n*n; break;
case 5: type = HELMHOLTZ_2; dim = n*n; break;
default: type = TEST_1; dim = n;
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,dim);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr);
use_random = 1;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-norandom",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
use_random = 0;
ierr = VecSet(u,pfive);CHKERRQ(ierr);
} else {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
}
/* Create and assemble matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = FormTestMatrix(A,n,type);CHKERRQ(ierr);
ierr = MatMult(A,u,b);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-printout",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Create KSP context; set operators and options; solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
ierr = KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* Check error */
ierr = VecAXPY(x,none,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G,Iterations %D\n",norm,its);CHKERRQ(ierr);
/* Free work space */
ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
typedef enum {RANDOM, CONSTANT, TANH, NUM_FUNCS} FuncType;
const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
Mat A;
PetscMPIInt size;
PetscInt n = 10,N,ndim=4,dim[4],DIM,i;
Vec x,y,z;
PetscScalar s;
PetscRandom rdm;
PetscReal enorm;
PetscInt func;
FuncType function = RANDOM;
PetscBool view = PETSC_FALSE;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uniprocessor example only!");
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, PETSC_NULL, "FFTW Options", "ex112");CHKERRQ(ierr);
ierr = PetscOptionsEList("-function", "Function type", "ex112", funcNames, NUM_FUNCS, funcNames[function], &func, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the functions", "ex112", view, &view, PETSC_NULL);CHKERRQ(ierr);
function = (FuncType) func;
ierr = PetscOptionsEnd();CHKERRQ(ierr);
for (DIM = 0; DIM < ndim; DIM++){
dim[DIM] = n; /* size of transformation in DIM-dimension */
}
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
for (DIM = 1; DIM < 5; DIM++){
for (i = 0, N = 1; i < DIM; i++) N *= dim[i];
ierr = PetscPrintf(PETSC_COMM_SELF, "\n %d-D: FFTW on vector of size %d \n",DIM,N);CHKERRQ(ierr);
/* create FFTW object */
ierr = MatCreateFFT(PETSC_COMM_SELF,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
/* create vectors of length N=n^DIM */
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* set values of space vector x */
if (function == RANDOM) {
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
} else if (function == CONSTANT) {
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
} else if (function == TANH) {
PetscScalar *a;
ierr = VecGetArray(x, &a);CHKERRQ(ierr);
for (i = 0; i < N; ++i) {
a[i] = tanh((i - N/2.0)*(10.0/N));
}
ierr = VecRestoreArray(x, &a);CHKERRQ(ierr);
}
if (view) {ierr = VecView(x, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
/* apply FFTW_FORWARD and FFTW_BACKWARD several times on same x, y, and z */
for (i=0; i<3; i++){
ierr = MatMult(A,x,y);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(y, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %G\n",enorm);CHKERRQ(ierr);
}
}
/* apply FFTW_FORWARD and FFTW_BACKWARD several times on different x */
for (i=0; i<3; i++){
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&x);CHKERRQ(ierr);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of new |x - z| %G\n",enorm);CHKERRQ(ierr);
}
}
/* free spaces */
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=3,N1=3,N2=3,N=N0*N1*N2;
PetscRandom rdm;
PetscScalar a;
PetscReal enorm;
Vec x,y,z,input,output;
PetscBool view=PETSC_FALSE,use_interface=PETSC_TRUE;
Mat A;
PetscInt DIM, dim[3],vsize;
PetscReal fac;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires real numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&input);CHKERRQ(ierr);
ierr = VecSetSizes(input,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(input);CHKERRQ(ierr);
ierr = VecSetRandom(input,rdm);CHKERRQ(ierr);
ierr = VecDuplicate(input,&output);
// ierr = VecGetSize(input,&vsize);CHKERRQ(ierr);
// printf("Size of the input Vector is %d\n",vsize);
DIM = 3;
dim[0] = N0; dim[1] = N1; dim[2] = N2;
ierr = MatCreateFFT(PETSC_COMM_WORLD,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetSize(y,&vsize);CHKERRQ(ierr);
printf("The vector size from the main routine is %d\n",vsize);
ierr = InputTransformFFT(A,input,x);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
ierr = OutputTransformFFT(A,z,output);CHKERRQ(ierr);
fac = 1.0/(PetscReal)N;
ierr = VecScale(output,fac);CHKERRQ(ierr);
ierr = VecAssemblyBegin(input);CHKERRQ(ierr);
ierr = VecAssemblyEnd(input);CHKERRQ(ierr);
ierr = VecAssemblyBegin(output);CHKERRQ(ierr);
ierr = VecAssemblyEnd(output);CHKERRQ(ierr);
ierr = VecView(input,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(output,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecAXPY(output,-1.0,input);CHKERRQ(ierr);
ierr = VecNorm(output,NORM_1,&enorm);CHKERRQ(ierr);
// if (enorm > 1.e-14){
if (!rank)
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
// }
// ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
// printf("Vector size from ex148 %d\n",vsize);
// ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
// ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
// ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscMPIInt size;
PetscErrorCode ierr;
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA,sB,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
PetscReal norm1,norm2,rnorm,tol=PETSC_SMALL;
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm, iscol;
PetscRandom rdm;
PetscBool doIcc=PETSC_TRUE,equal;
MatInfo minfo1,minfo2;
MatFactorInfo factinfo;
MatType type;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
ierr = MatGetType(sA,&type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0;
col[0] = n-1; col[1] = 1; col[2] = 0;
value[0] = 0.1; value[1] = -1.0; value[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatGetInfo() of A and sA */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
}
/* Test MatDuplicate() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
if (i-Ii) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
/* Scaling matrix with complex numbers results non-spd matrix,
causing crash of MatForwardSolve() and MatBackwardSolve() */
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
if (norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
}
{
PetscScalar alpha=0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sB,alpha);CHKERRQ(ierr);
}
#endif
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
}
/* Test MatMult() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sB,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
norm1 = tol;
inc = bs;
/* initialize factinfo */
ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);
for (lf=-1; lf<10; lf += inc) {
if (lf==-1) { /* Cholesky factor of sB (duplicate sA) */
factinfo.fill = 5.0;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
} else if (!doIcc) break;
else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lf;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
/* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */
/* test MatGetDiagonal on numeric factor */
/*
if (lf == -1) {
ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
printf(" in ex74.c, diag: \n");
ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
*/
ierr = MatMult(sB,x,b);CHKERRQ(ierr);
/* test MatForwardSolve() and MatBackwardSolve() */
if (lf == -1) {
ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
if (10*norm1 < norm2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
}
}
/* test MatSolve() */
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
/* printf("lf: %d, error: %G\n", lf,norm2); */
if (10*norm1 < norm2 && lf-inc != -1) {
ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
}
norm1 = norm2;
if (norm2 < tol && lf != -1) break;
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sB);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int Argc,char **Args)
{
PetscBool flg;
PetscInt n = -6;
PetscScalar rho = 1.0;
PetscReal h;
PetscReal beta = 1.0;
DM da;
PetscRandom rctx;
PetscMPIInt comm_size;
Mat H,HtH;
PetscInt x, y, xs, ys, xm, ym;
PetscReal r1, r2;
PetscScalar uxy1, uxy2;
MatStencil sxy, sxy_m;
PetscScalar val, valconj;
Vec b, Htb,xvec;
KSP kspmg;
PC pcmg;
PetscErrorCode ierr;
PetscInt ix[1] = {0};
PetscScalar vals[1] = {1.0};
PetscInitialize(&Argc,&Args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-size",&n,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-beta",&beta,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,"-rho",&rho,&flg);CHKERRQ(ierr);
/* Set the fudge parameters, we scale the whole thing by 1/(2*h) later */
h = 1.;
rho *= 1./(2.*h);
/* Geometry info */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC, DMDA_STENCIL_STAR, n, n,
PETSC_DECIDE, PETSC_DECIDE, 2 /* this is the # of dof's */,
1, NULL, NULL, &da);CHKERRQ(ierr);
/* Random numbers */
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
/* Single or multi processor ? */
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&comm_size);CHKERRQ(ierr);
/* construct matrix */
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &H);CHKERRQ(ierr);
/* get local corners for this processor */
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
/* Assemble the matrix */
for (x=xs; x<xs+xm; x++) {
for (y=ys; y<ys+ym; y++) {
/* each lattice point sets only the *forward* pointing parameters (right, down),
i.e. Nabla_1^+ and Nabla_2^+.
In this way we can use only local random number creation. That means
we also have to set the corresponding backward pointing entries. */
/* Compute some normally distributed random numbers via Box-Muller */
ierr = PetscRandomGetValueReal(rctx, &r1);CHKERRQ(ierr);
r1 = 1.-r1; /* to change from [0,1) to (0,1], which we need for the log */
ierr = PetscRandomGetValueReal(rctx, &r2);CHKERRQ(ierr);
PetscReal R = PetscSqrtReal(-2.*PetscLogReal(r1));
PetscReal c = PetscCosReal(2.*PETSC_PI*r2);
PetscReal s = PetscSinReal(2.*PETSC_PI*r2);
/* use those to set the field */
uxy1 = PetscExpScalar(((PetscScalar) (R*c/beta))*PETSC_i);
uxy2 = PetscExpScalar(((PetscScalar) (R*s/beta))*PETSC_i);
sxy.i = x; sxy.j = y; /* the point where we are */
/* center action */
sxy.c = 0; /* spin 0, 0 */
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &rho, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; /* spin 1, 1 */
val = -rho;
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x+1; sxy_m.j = y; /* right action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x; sxy_m.j = y+1; /* down action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = PetscConj(uxy2); valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* scale H */
ierr = MatScale(H, 1./(2.*h));CHKERRQ(ierr);
/* it looks like H is Hermetian */
/* construct normal equations */
ierr = MatMatMult(H, H, MAT_INITIAL_MATRIX, 1., &HtH);CHKERRQ(ierr);
/* permutation matrix to check whether H and HtH are identical to the ones in the paper */
/* Mat perm; */
/* ierr = DMCreateMatrix(da, &perm);CHKERRQ(ierr); */
/* PetscInt row, col; */
/* PetscScalar one = 1.0; */
/* for (PetscInt i=0; i<n; i++) { */
/* for (PetscInt j=0; j<n; j++) { */
/* row = (i*n+j)*2; col = i*n+j; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* row = (i*n+j)*2+1; col = i*n+j + n*n; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* } */
/* } */
/* ierr = MatAssemblyBegin(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* ierr = MatAssemblyEnd(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* Mat Hperm; */
/* ierr = MatPtAP(H, perm, MAT_INITIAL_MATRIX, 1.0, &Hperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix H after construction\n");CHKERRQ(ierr); */
/* ierr = MatView(Hperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* Mat HtHperm; */
/* ierr = MatPtAP(HtH, perm, MAT_INITIAL_MATRIX, 1.0, &HtHperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix HtH:\n");CHKERRQ(ierr); */
/* ierr = MatView(HtHperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* right hand side */
ierr = DMCreateGlobalVector(da, &b);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
ierr = VecSetValues(b, 1, ix, vals, INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* ierr = VecSetRandom(b, rctx);CHKERRQ(ierr); */
ierr = VecDuplicate(b, &Htb);CHKERRQ(ierr);
ierr = MatMultTranspose(H, b, Htb);CHKERRQ(ierr);
/* construct solver */
ierr = KSPCreate(PETSC_COMM_WORLD,&kspmg);CHKERRQ(ierr);
ierr = KSPSetType(kspmg, KSPCG);CHKERRQ(ierr);
ierr = KSPGetPC(kspmg,&pcmg);CHKERRQ(ierr);
ierr = PCSetType(pcmg,PCASA);CHKERRQ(ierr);
/* maybe user wants to override some of the choices */
ierr = KSPSetFromOptions(kspmg);CHKERRQ(ierr);
ierr = KSPSetOperators(kspmg, HtH, HtH, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = DMDASetRefinementFactor(da, 3, 3, 3);CHKERRQ(ierr);
ierr = PCSetDM(pcmg,da);CHKERRQ(ierr);
ierr = PCASASetTolerances(pcmg, 1.e-6, 1.e-10,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
ierr = VecDuplicate(b, &xvec);CHKERRQ(ierr);
ierr = VecSet(xvec, 0.0);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(kspmg, Htb, xvec);CHKERRQ(ierr);
/* ierr = VecView(xvec, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
ierr = KSPDestroy(&kspmg);CHKERRQ(ierr);
ierr = VecDestroy(&xvec);CHKERRQ(ierr);
/* seems to be destroyed by KSPDestroy */
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&Htb);CHKERRQ(ierr);
ierr = MatDestroy(&HtH);CHKERRQ(ierr);
ierr = MatDestroy(&H);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=10,N1=10,N2=10,N3=10,N4=10,N=N0*N1*N2*N3*N4;
PetscRandom rdm;
PetscReal enorm;
Vec x,y,z,input,output;
Mat A;
PetscInt DIM, dim[5],vsize;
PetscReal fac;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
if (size!=1)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uni-processor example only");
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_SELF,&input);CHKERRQ(ierr);
ierr = VecSetSizes(input,N,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(input);CHKERRQ(ierr);
ierr = VecSetRandom(input,rdm);CHKERRQ(ierr);
ierr = VecDuplicate(input,&output);
DIM = 5; dim[0] = N0; dim[1] = N1; dim[2] = N2; dim[3] = N3; dim[4] = N4;
ierr = MatCreateFFT(PETSC_COMM_SELF,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetSize(x,&vsize);CHKERRQ(ierr);
printf("The vector size of input from the main routine is %d\n",vsize);
ierr = VecGetSize(z,&vsize);CHKERRQ(ierr);
printf("The vector size of output from the main routine is %d\n",vsize);
ierr = InputTransformFFT(A,input,x);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
ierr = OutputTransformFFT(A,z,output);CHKERRQ(ierr);
fac = 1.0/(PetscReal)N;
ierr = VecScale(output,fac);CHKERRQ(ierr);
/*
ierr = VecAssemblyBegin(input);CHKERRQ(ierr);
ierr = VecAssemblyEnd(input);CHKERRQ(ierr);
ierr = VecAssemblyBegin(output);CHKERRQ(ierr);
ierr = VecAssemblyEnd(output);CHKERRQ(ierr);
ierr = VecView(input,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(output,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
*/
ierr = VecAXPY(output,-1.0,input);CHKERRQ(ierr);
ierr = VecNorm(output,NORM_1,&enorm);CHKERRQ(ierr);
// if (enorm > 1.e-14){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
// }
ierr = VecDestroy(&output);CHKERRQ(ierr);
ierr = VecDestroy(&input);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
Mat A,B,C,D;
PetscInt i,M=10,N=5,j,nrows,ncols,am,an,rstart,rend;
PetscErrorCode ierr;
PetscRandom r;
PetscBool equal,iselemental;
PetscReal fill = 1.0;
IS isrows,iscols;
const PetscInt *rows,*cols;
PetscScalar *v,rval;
#if defined(PETSC_HAVE_ELEMENTAL)
PetscBool Test_MatMatMult=PETSC_TRUE;
#else
PetscBool Test_MatMatMult=PETSC_FALSE;
#endif
PetscMPIInt size;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
/* Set local matrix entries */
ierr = MatGetOwnershipIS(A,&isrows,&iscols);CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(nrows*ncols,&v);CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
ierr = PetscRandomGetValue(r,&rval);CHKERRQ(ierr);
v[i*ncols+j] = rval;
}
}
ierr = MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&iscols);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
/* Test MatTranspose() */
ierr = MatCreateTranspose(A,&C);CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr); /* B = A^T */
ierr = MatMultEqual(C,B,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A^T*x != (x^T*A)^T");
ierr = MatTranspose(A,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr); /* B = A^T */
ierr = MatMultEqual(C,B,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A^T*x != (x^T*A)^T");
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
ierr = MatTranspose(B,MAT_INPLACE_MATRIX,&B);CHKERRQ(ierr);
ierr = MatMultEqual(C,B,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A^T*x != (x^T*A)^T");
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
/* Test MatMatMult() */
if (Test_MatMatMult) {
#if !defined(PETSC_HAVE_ELEMENTAL)
if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This test requires ELEMENTAL");
#endif
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr); /* B = A^T */
ierr = MatMatMult(B,A,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr); /* C = B*A = A^T*A */
ierr = MatMatMult(B,A,MAT_REUSE_MATRIX,fill,&C);CHKERRQ(ierr);
/* Test MatDuplicate for matrix product */
ierr = MatDuplicate(C,MAT_COPY_VALUES,&D);CHKERRQ(ierr);
ierr = MatDestroy(&D);CHKERRQ(ierr);
/* Test B*A*x = C*x for n random vector x */
ierr = MatMatMultEqual(B,A,C,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"B*A*x != C*x");
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatMatMultSymbolic(B,A,fill,&C);CHKERRQ(ierr);
for (i=0; i<2; i++) {
/* Repeat the numeric product to test reuse of the previous symbolic product */
ierr = MatMatMultNumeric(B,A,C);CHKERRQ(ierr);
ierr = MatMatMultEqual(B,A,C,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"B*A*x != C*x");
}
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
/* Test MatTransposeMatMult() */
ierr = PetscObjectTypeCompare((PetscObject)A,MATELEMENTAL,&iselemental);CHKERRQ(ierr);
if (!iselemental) {
ierr = MatTransposeMatMult(A,A,MAT_INITIAL_MATRIX,fill,&D);CHKERRQ(ierr); /* D = A^T*A */
ierr = MatTransposeMatMult(A,A,MAT_REUSE_MATRIX,fill,&D);CHKERRQ(ierr);
/* Test MatDuplicate for matrix product */
ierr = MatDuplicate(D,MAT_COPY_VALUES,&C);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
/* ierr = MatView(D,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
ierr = MatTransposeMatMultEqual(A,A,D,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"D*x != A^T*A*x");
ierr = MatDestroy(&D);CHKERRQ(ierr);
/* Test D*x = A^T*C*A*x, where C is in AIJ format */
ierr = MatGetLocalSize(A,&am,&an);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
if (size == 1) {
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,am,am);CHKERRQ(ierr);
} else {
ierr = MatSetSizes(C,am,am,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
}
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
v[0] = 1.0;
for (i=rstart; i<rend; i++) {
ierr = MatSetValues(C,1,&i,1,&i,v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* B = C*A, D = A^T*B */
ierr = MatMatMult(C,A,MAT_INITIAL_MATRIX,1.0,&B);CHKERRQ(ierr);
ierr = MatTransposeMatMult(A,B,MAT_INITIAL_MATRIX,fill,&D);CHKERRQ(ierr);
ierr = MatTransposeMatMultEqual(A,B,D,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"D*x != A^T*B*x");
ierr = MatDestroy(&D);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
Mat A,B,C,D;
PetscInt i,M=10,N=5,j,nrows,ncols;
PetscErrorCode ierr;
PetscRandom r;
PetscBool equal,iselemental;
PetscReal fill = 1.0;
IS isrows,iscols;
const PetscInt *rows,*cols;
PetscScalar *v,rval;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
/* Set local matrix entries */
ierr = MatGetOwnershipIS(A,&isrows,&iscols);CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);CHKERRQ(ierr);
ierr = PetscMalloc(nrows*ncols*sizeof(*v),&v);CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
ierr = PetscRandomGetValue(r,&rval);CHKERRQ(ierr);
v[i*ncols+j] = rval;
}
}
ierr = MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&iscols);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
/* Test MatMatMult() */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr); /* B = A^T */
ierr = MatMatMult(B,A,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr); /* C = B*A = A^T*A */
ierr = MatMatMultSymbolic(B,A,fill,&D);CHKERRQ(ierr); /* D = B*A = A^T*A */
for (i=0; i<2; i++) {
/* Repeat the numeric product to test reuse of the previous symbolic product */
ierr = MatMatMultNumeric(B,A,D);CHKERRQ(ierr);
}
ierr = MatMultEqual(C,D,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"C != D");
ierr = MatDestroy(&D);CHKERRQ(ierr);
/* Test MatTransposeMatMult() */
ierr = PetscObjectTypeCompare((PetscObject)A,MATELEMENTAL,&iselemental);CHKERRQ(ierr);
if (!iselemental) {
ierr = MatTransposeMatMult(A,A,MAT_INITIAL_MATRIX,fill,&D);CHKERRQ(ierr); /* D = A^T*A */
ierr = MatEqual(C,D,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"C != D");
ierr = MatDestroy(&D);CHKERRQ(ierr);
}
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&B);
ierr = MatDestroy(&A);
PetscFinalize();
return(0);
}
int main(int argc,char **argv)
{
PetscMPIInt rank,size;
PetscInt N = 6,M=8,P=5,dof=1;
PetscInt stencil_width=1,pt=0,st=0;
PetscErrorCode ierr;
PetscBool flg2,flg3,isbinary,mpiio;
DMBoundaryType bx = DM_BOUNDARY_NONE,by = DM_BOUNDARY_NONE,bz = DM_BOUNDARY_NONE;
DMDAStencilType stencil_type = DMDA_STENCIL_STAR;
DM da,da2;
Vec global1,global2;
PetscScalar mone = -1.0;
PetscReal norm;
PetscViewer viewer;
PetscRandom rdm;
#if defined(PETSC_HAVE_HDF5)
PetscBool ishdf5;
#endif
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-P",&P,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-dof",&dof,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-stencil_width",&stencil_width,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-periodic",&pt,NULL);CHKERRQ(ierr);
if (pt == 1) bx = DM_BOUNDARY_PERIODIC;
if (pt == 2) by = DM_BOUNDARY_PERIODIC;
if (pt == 4) {bx = DM_BOUNDARY_PERIODIC; by = DM_BOUNDARY_PERIODIC;}
ierr = PetscOptionsGetInt(NULL,NULL,"-stencil_type",&st,NULL);CHKERRQ(ierr);
stencil_type = (DMDAStencilType) st;
ierr = PetscOptionsHasName(NULL,NULL,"-oned",&flg2);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-twod",&flg2);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-threed",&flg3);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-binary",&isbinary);CHKERRQ(ierr);
#if defined(PETSC_HAVE_HDF5)
ierr = PetscOptionsHasName(NULL,NULL,"-hdf5",&ishdf5);CHKERRQ(ierr);
#endif
ierr = PetscOptionsHasName(NULL,NULL,"-mpiio",&mpiio);CHKERRQ(ierr);
if (flg2) {
ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,stencil_type,M,N,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,0,0,&da);CHKERRQ(ierr);
} else if (flg3) {
ierr = DMDACreate3d(PETSC_COMM_WORLD,bx,by,bz,stencil_type,M,N,P,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,0,0,0,&da);CHKERRQ(ierr);
} else {
ierr = DMDACreate1d(PETSC_COMM_WORLD,bx,M,dof,stencil_width,NULL,&da);CHKERRQ(ierr);
}
ierr = DMCreateGlobalVector(da,&global1);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)global1,"Test_Vec");CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecSetRandom(global1,rdm);CHKERRQ(ierr);
if (isbinary) {
if (mpiio) {
ierr = PetscOptionsSetValue(NULL,"-viewer_binary_mpiio","");CHKERRQ(ierr);
}
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"temp",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
#if defined(PETSC_HAVE_HDF5)
} else if (ishdf5) {
ierr = PetscViewerHDF5Open(PETSC_COMM_WORLD,"temp",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
#endif
} else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Invalid Viewer : Run with -binary or -hdf5 option\n");
ierr = VecView(global1,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Global vector written to temp file is \n");CHKERRQ(ierr);
ierr = VecView(global1,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
if (flg2) {
ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,stencil_type,M,N,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,0,0,&da2);CHKERRQ(ierr);
} else if (flg3) {
ierr = DMDACreate3d(PETSC_COMM_WORLD,bx,by,bz,stencil_type,M,N,P,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,0,0,0,&da2);CHKERRQ(ierr);
} else {
ierr = DMDACreate1d(PETSC_COMM_WORLD,bx,M,dof,stencil_width,NULL,&da2);CHKERRQ(ierr);
}
if (isbinary) {
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"temp",FILE_MODE_READ,&viewer);CHKERRQ(ierr);
#if defined(PETSC_HAVE_HDF5)
} else if (ishdf5) {
ierr = PetscViewerHDF5Open(PETSC_COMM_WORLD,"temp",FILE_MODE_READ,&viewer);CHKERRQ(ierr);
#endif
} else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Invalid Viewer : Run with -binary or -hdf5 option\n");
ierr = DMCreateGlobalVector(da2,&global2);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)global2,"Test_Vec");CHKERRQ(ierr);
ierr = VecLoad(global2,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Global vector read from temp file is \n");CHKERRQ(ierr);
ierr = VecView(global2,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecAXPY(global2,mone,global1);CHKERRQ(ierr);
ierr = VecNorm(global2,NORM_MAX,&norm);CHKERRQ(ierr);
if (norm != 0.0) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"ex23: Norm of difference %g should be zero\n",(double)norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," Number of processors %d\n",size);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," M,N,P,dof %D %D %D %D\n",M,N,P,dof);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," stencil_width %D stencil_type %d periodic %d\n",stencil_width,(int)stencil_type,(int)pt);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," dimension %d\n",1 + (int) flg2 + (int) flg3);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = DMDestroy(&da2);CHKERRQ(ierr);
ierr = VecDestroy(&global1);CHKERRQ(ierr);
ierr = VecDestroy(&global2);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int test1(void)
{
PetscLogDouble t1,t2;
double value;
int i,ierr,*z,*zi,intval;
PetscScalar *x,*y;
PetscRandom r;
ierr = PetscRandomCreate(PETSC_COMM_SELF,&r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
ierr = PetscMalloc(20000*sizeof(PetscScalar),&x);CHKERRQ(ierr);
ierr = PetscMalloc(20000*sizeof(PetscScalar),&y);CHKERRQ(ierr);
ierr = PetscMalloc(2000*sizeof(int),&z);CHKERRQ(ierr);
ierr = PetscMalloc(2000*sizeof(int),&zi);CHKERRQ(ierr);
/* Take care of paging effects */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
/* Form the random set of integers */
for (i=0; i<2000; i++) {
ierr = PetscRandomGetValue(r,&value);CHKERRQ(ierr);
intval = (int)(value*20000.0);
z[i] = intval;
}
for (i=0; i<2000; i++) {
ierr = PetscRandomGetValue(r,&value);CHKERRQ(ierr);
intval = (int)(value*20000.0);
zi[i] = intval;
}
/* fprintf(stdout,"Done setup\n"); */
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { x[i] = y[i]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[i]",(t2-t1)/2000.0);
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<500; i+=4) {
x[i] = y[z[i]];
x[1+i] = y[z[1+i]];
x[2+i] = y[z[2+i]];
x[3+i] = y[z[3+i]];
}
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[idx[i]] - unroll 4",(t2-t1)/2000.0);
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr)
for (i=0; i<2000; i++) { x[i] = y[z[i]]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[idx[i]]",(t2-t1)/2000.0);
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<1000; i+=2) { x[i] = y[z[i]]; x[1+i] = y[z[1+i]]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[idx[i]] - unroll 2",(t2-t1)/2000.0);
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { x[z[i]] = y[i]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[z[i]] = y[i]",(t2-t1)/2000.0);
ierr = BlastCache();CHKERRQ(ierr);
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { x[z[i]] = y[zi[i]]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[z[i]] = y[zi[i]]",(t2-t1)/2000.0);
ierr = PetscMemcpy(x,y,10);CHKERRQ(ierr);
ierr = PetscMemcpy(z,zi,10);CHKERRQ(ierr);
ierr = PetscFree(z);CHKERRQ(ierr);
ierr = PetscFree(zi);CHKERRQ(ierr);
ierr = PetscFree(x);CHKERRQ(ierr);
ierr = PetscFree(y);CHKERRQ(ierr);
PetscRandomDestroy(r);
PetscFunctionReturn(0);
}
int test2(void)
{
PetscLogDouble t1,t2;
double value;
int i,ierr,z[20000],zi[20000],intval,tmp;
PetscScalar x[20000],y[20000];
PetscRandom r;
ierr = PetscRandomCreate(PETSC_COMM_SELF,&r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
/* Take care of paging effects */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<20000; i++) {
x[i] = i;
y[i] = i;
z[i] = i;
zi[i] = i;
}
/* Form the random set of integers */
for (i=0; i<20000; i++) {
ierr = PetscRandomGetValue(r,&value);CHKERRQ(ierr);
intval = (int)(value*20000.0);
tmp = z[i];
z[i] = z[intval];
z[intval] = tmp;
}
for (i=0; i<20000; i++) {
ierr = PetscRandomGetValue(r,&value);CHKERRQ(ierr);
intval = (int)(value*20000.0);
tmp = zi[i];
zi[i] = zi[intval];
zi[intval] = tmp;
}
/* fprintf(stdout,"Done setup\n"); */
/* ierr = BlastCache();CHKERRQ(ierr); */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { x[i] = y[i]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[i]",(t2-t1)/2000.0);
/* ierr = BlastCache();CHKERRQ(ierr); */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { y[i] = x[z[i]]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[i] = y[idx[i]]",(t2-t1)/2000.0);
/* ierr = BlastCache();CHKERRQ(ierr); */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { x[z[i]] = y[i]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[z[i]] = y[i]",(t2-t1)/2000.0);
/* ierr = BlastCache();CHKERRQ(ierr); */
ierr = PetscGetTime(&t1);CHKERRQ(ierr);
for (i=0; i<2000; i++) { y[z[i]] = x[zi[i]]; }
ierr = PetscGetTime(&t2);CHKERRQ(ierr);
fprintf(stdout,"%-27s : %e sec\n","x[z[i]] = y[zi[i]]",(t2-t1)/2000.0);
PetscRandomDestroy(r);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
Mat A,B,C,D;
PetscInt i,j,k,M=10,N=5;
PetscScalar *array,*a;
PetscErrorCode ierr;
PetscRandom r;
PetscTruth equal=PETSC_FALSE;
PetscReal fill = 1.0;
PetscInt rstart,rend,nza,col,am,an,bm,bn;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-N",&N,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-fill",&fill,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
/* create a aij matrix A */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,M);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
nza = (PetscInt)(.3*M); /* num of nozeros in each row of A */
ierr = MatSeqAIJSetPreallocation(A,nza,PETSC_NULL);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(A,nza,PETSC_NULL,nza,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
ierr = PetscMalloc((nza+1)*sizeof(PetscScalar),&a);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
for (j=0; j<nza; j++) {
ierr = PetscRandomGetValue(r,&a[j]);CHKERRQ(ierr);
col = (PetscInt)(M*PetscRealPart(a[j]));
ierr = MatSetValues(A,1,&i,1,&col,&a[j],ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* create a dense matrix B */
ierr = MatGetLocalSize(A,&am,&an);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&B);CHKERRQ(ierr);
ierr = MatSetSizes(B,PETSC_DECIDE,am,N,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(B,MATDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(B,PETSC_NULL);CHKERRQ(ierr);
ierr = MatMPIDenseSetPreallocation(B,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetLocalSize(B,&bm,&bn);CHKERRQ(ierr);
ierr = MatGetArray(B,&array);CHKERRQ(ierr);
k = 0;
for (j=0; j<N; j++){ /* local column-wise entries */
for (i=0; i<bm; i++){
ierr = PetscRandomGetValue(r,&array[k++]);CHKERRQ(ierr);
}
}
ierr = MatRestoreArray(B,&array);CHKERRQ(ierr);
ierr = PetscRandomDestroy(r);CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatMatMult() */
ierr = MatMatMult(B,A,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr);
/*
ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_MATLAB);
ierr = MatView(C,0);CHKERRQ(ierr);
ierr = MatView(B,0);CHKERRQ(ierr);
ierr = MatView(A,0);CHKERRQ(ierr);
*/
ierr = MatMatMultSymbolic(B,A,fill,&D);CHKERRQ(ierr);
for (i=0; i<2; i++){
ierr = MatMatMultNumeric(B,A,D);CHKERRQ(ierr);
}
ierr = MatEqual(C,D,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"C != D");
ierr = MatDestroy(D);CHKERRQ(ierr);
ierr = MatDestroy(C);CHKERRQ(ierr);
ierr = MatDestroy(B);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = PetscFree(a);CHKERRQ(ierr);
PetscFinalize();
return(0);
}
int main(int argc,char **args)
{
Mat A,B;
Vec xx,s1,s2,yy;
PetscErrorCode ierr;
PetscInt m=45,rows[2],cols[2],bs=1,i,row,col,*idx,M;
PetscScalar rval,vals1[4],vals2[4];
PetscRandom rdm;
IS is1,is2;
PetscReal s1norm,s2norm,rnorm,tol = 1.e-4;
PetscTruth flg;
MatFactorInfo info;
PetscInitialize(&argc,&args,(char *)0,help);
/* Test MatSetValues() and MatGetValues() */
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_block_size",&bs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_size",&m,PETSC_NULL);CHKERRQ(ierr);
M = m*bs;
ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,bs,M,M,1,PETSC_NULL,&A);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,M,M,15,PETSC_NULL,&B);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,M,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&yy);CHKERRQ(ierr);
/* For each row add atleast 15 elements */
for (row=0; row<M; row++) {
for (i=0; i<25*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
col = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatSetValues(A,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Now set blocks of values */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[0] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[1] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[2] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[3] = rval;
ierr = MatSetValues(A,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_INFINITY,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_1,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_NORM_1()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
/* MatShift() */
rval = 10*s1norm;
ierr = MatShift(A,rval);CHKERRQ(ierr);
ierr = MatShift(B,rval);CHKERRQ(ierr);
/* Test MatTranspose() */
ierr = MatTranspose(A,MAT_REUSE_MATRIX,&A);CHKERRQ(ierr);
ierr = MatTranspose(B,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);
/* Now do MatGetValues() */
for (i=0; i<30; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatGetValues(A,2,rows,2,cols,vals1);CHKERRQ(ierr);
ierr = MatGetValues(B,2,rows,2,cols,vals2);CHKERRQ(ierr);
ierr = PetscMemcmp(vals1,vals2,4*sizeof(PetscScalar),&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetValues bs = %D\n",bs);CHKERRQ(ierr);
}
}
/* Test MatMult(), MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSet(s2,0.0);CHKERRQ(ierr);
ierr = MatMult(A,xx,s1);CHKERRQ(ierr);
ierr = MatMultAdd(A,xx,s2,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatMult not equal to MatMultAdd Norm1=%e Norm2=%e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatMult() */
ierr = MatMultEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult()\n");CHKERRQ(ierr);
}
/* Test MatMultAdd() */
ierr = MatMultAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultAdd()\n");CHKERRQ(ierr);
}
/* Test MatMultTranspose() */
ierr = MatMultTransposeEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTranspose()\n");CHKERRQ(ierr);
}
/* Test MatMultTransposeAdd() */
ierr = MatMultTransposeAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTransposeAdd()\n");CHKERRQ(ierr);
}
/* Do LUFactor() on both the matrices */
ierr = PetscMalloc(M*sizeof(PetscInt),&idx);CHKERRQ(ierr);
for (i=0; i<M; i++) idx[i] = i;
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,&is1);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,&is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = ISSetPermutation(is1);CHKERRQ(ierr);
ierr = ISSetPermutation(is2);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
info.fill = 2.0;
info.dtcol = 0.0;
info.zeropivot = 1.e-14;
info.pivotinblocks = 1.0;
ierr = MatLUFactor(B,is1,is2,&info);CHKERRQ(ierr);
ierr = MatLUFactor(A,is1,is2,&info);CHKERRQ(ierr);
/* Test MatSolveAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(yy,rdm);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,yy,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,yy,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveAdd() when x = A'b +x */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(s1,rdm);CHKERRQ(ierr);
ierr = VecCopy(s2,s1);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,s2,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,s1,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd(same) - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolve() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolve(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolve(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolve - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveTranspose() */
if (bs < 8) {
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolveTranspose(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolveTranspose(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveTranspose - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(B);CHKERRQ(ierr);
ierr = VecDestroy(xx);CHKERRQ(ierr);
ierr = VecDestroy(s1);CHKERRQ(ierr);
ierr = VecDestroy(s2);CHKERRQ(ierr);
ierr = VecDestroy(yy);CHKERRQ(ierr);
ierr = ISDestroy(is1);CHKERRQ(ierr);
ierr = ISDestroy(is2);CHKERRQ(ierr);
ierr = PetscRandomDestroy(rdm);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscReal norm; /* norm of solution error */
PetscInt dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
PetscErrorCode ierr;
PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
PetscRandom rctx;
PetscReal h2,sigma1 = 100.0;
PetscBool flg = PETSC_FALSE;
PetscScalar a = 1.0+PETSC_i;
PetscInitialize(&argc,&args,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
a=1.0+PETSC_i;
printf("%g+%gi\n",(double)PetscRealPart(a),(double)PetscImaginaryPart(a));
ierr = PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
dim = n*n;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix is
determined by PETSc at runtime.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/*
Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors. Determine which
rows of the matrix are locally owned.
*/
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
/*
Set matrix elements in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Always specify global rows and columns of matrix entries.
*/
ierr = PetscOptionsGetBool(NULL,"-norandom",&flg,NULL);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2 + sigma2*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Create parallel vectors.
- When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
we specify only the vector's global
dimension; the parallel partitioning is determined at runtime.
- Note: We form 1 vector from scratch and then duplicate as needed.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,dim);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
*/
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,pfive);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Print the first 3 entries of x; this demonstrates extraction of the
real and imaginary components of the complex vector, x.
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-print_x3",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = VecGetArray(x,&xa);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");CHKERRQ(ierr);
for (i=0; i<3; i++) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));CHKERRQ(ierr);
}
ierr = VecRestoreArray(x,&xa);CHKERRQ(ierr);
}
/*
Check the error
*/
ierr = VecAXPY(x,none,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 2;
AppCtx ctx;
PetscScalar *u;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");CHKERRQ(ierr);
{
ctx.omega_s = 1.0;
ierr = PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL);CHKERRQ(ierr);
ctx.H = 1.0;
ierr = PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
ctx.E = 1.0;
ierr = PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL);CHKERRQ(ierr);
ctx.V = 1.0;
ierr = PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL);CHKERRQ(ierr);
ctx.X = 1.0;
ierr = PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL);CHKERRQ(ierr);
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = 1;
u[1] = .7;
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ctx.rand);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,100000,2000.0);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ctx.rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Vec x,y,u,s1,s2;
Mat A,sA,sB;
PetscRandom rctx;
PetscReal r1,r2,rnorm,tol = PETSC_SQRT_MACHINE_EPSILON;
PetscScalar one=1.0, neg_one=-1.0, value[3], four=4.0,alpha=0.1;
PetscInt n,col[3],n1,block,row,i,j,i2,j2,Ii,J,rstart,rend,bs=1,mbs=16,d_nz=3,o_nz=3,prob=2;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscBool flg;
MatType type;
ierr = PetscInitialize(&argc,&args,(char*)0,help);
if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);
CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);
CHKERRQ(ierr);
n = mbs*bs;
/* Assemble MPISBAIJ matrix sA */
ierr = MatCreate(PETSC_COMM_WORLD,&sA);
CHKERRQ(ierr);
ierr = MatSetSizes(sA,PETSC_DECIDE,PETSC_DECIDE,n,n);
CHKERRQ(ierr);
ierr = MatSetType(sA,MATSBAIJ);
CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);
CHKERRQ(ierr);
ierr = MatGetType(sA,&type);
CHKERRQ(ierr);
ierr = MatMPISBAIJSetPreallocation(sA,bs,d_nz,NULL,o_nz,NULL);
CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,d_nz,NULL);
CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
if (n1*n1 != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n must be a perfect square of n1");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatView() */
ierr = MatCreateBAIJ(PETSC_COMM_WORLD,bs,PETSC_DECIDE,PETSC_DECIDE,n,n,d_nz,NULL,o_nz,NULL,&A);
CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatGetSize(), MatGetLocalSize() */
ierr = MatGetSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetSize(A, &i2,&j2);
CHKERRQ(ierr);
i -= i2;
j -= j2;
if (i || j) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatGetLocalSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetLocalSize(A, &i2,&j2);
CHKERRQ(ierr);
i2 -= i;
j2 -= j;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetLocalSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* vectors */
/*--------------------*/
/* i is obtained from MatGetLocalSize() */
ierr = VecCreate(PETSC_COMM_WORLD,&x);
CHKERRQ(ierr);
ierr = VecSetSizes(x,i,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = VecSetFromOptions(x);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);
CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSet(u,one);
CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_FROBENIUS,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_INFINITY,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_INFINITY(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_1,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_1(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(sA,&rstart,&rend);
CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&i2,&j2);
CHKERRQ(ierr);
i2 -= rstart;
j2 -= rend;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MaGetOwnershipRange()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatDiagonalScale() */
ierr = MatDiagonalScale(A,x,x);
CHKERRQ(ierr);
ierr = MatDiagonalScale(sA,x,x);
CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
/* Test MatGetDiagonal(), MatScale() */
ierr = MatGetDiagonal(A,s1);
CHKERRQ(ierr);
ierr = MatGetDiagonal(sA,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDiagonalScale() or MatGetDiagonal(), r1=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatScale(A,alpha);
CHKERRQ(ierr);
ierr = MatScale(sA,alpha);
CHKERRQ(ierr);
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);
CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sA,s2,NULL);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetRowMaxAbs() \n");
CHKERRQ(ierr);
}
/* Test MatMult(), MatMultAdd() */
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatMultTranspose(), MatMultTransposeAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = MatMultTranspose(A,x,s1);
CHKERRQ(ierr);
ierr = MatMultTranspose(sA,x,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale(), err=%g\n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(y,rctx);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A,x,y,s1);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(sA,x,y,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd(), err=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
/* Test MatDuplicate() */
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);
CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_WORLD," Error in MatDuplicate(), sA != sB \n");
CHKERRQ(ierr);
CHKERRQ(ierr);
}
ierr = MatMultEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMult()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMultAdd(()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatDestroy(&sB);
CHKERRQ(ierr);
ierr = VecDestroy(&u);
CHKERRQ(ierr);
ierr = VecDestroy(&x);
CHKERRQ(ierr);
ierr = VecDestroy(&y);
CHKERRQ(ierr);
ierr = VecDestroy(&s1);
CHKERRQ(ierr);
ierr = VecDestroy(&s2);
CHKERRQ(ierr);
ierr = MatDestroy(&sA);
CHKERRQ(ierr);
ierr = MatDestroy(&A);
CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);
CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat A,Atrans,sA,*submatA,*submatsA;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt bs=1,mbs=10,ov=1,i,j,k,*rows,*cols,nd=2,*idx,rstart,rend,sz,M,N,Mbs;
PetscScalar *vals,rval,one=1.0;
IS *is1,*is2;
PetscRandom rand;
PetscBool flg,TestOverlap,TestSubMat,TestAllcols,test_sorted=PETSC_FALSE;
PetscInt vid = -1;
#if defined(PETSC_USE_LOG)
PetscLogStage stages[2];
#endif
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_block_size",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-ov",&ov,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-nd",&nd,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-view_id",&vid,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_overlap", &TestOverlap);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_submat", &TestSubMat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_allcols", &TestAllcols);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_sorted",&test_sorted,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,mbs*bs,mbs*bs,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(A,MATBAIJ);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
ierr = MatMPIBAIJSetPreallocation(A,bs,PETSC_DEFAULT,NULL,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
Mbs = M/bs;
ierr = PetscMalloc1(bs,&rows);CHKERRQ(ierr);
ierr = PetscMalloc1(bs,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(bs*bs,&vals);CHKERRQ(ierr);
ierr = PetscMalloc1(M,&idx);CHKERRQ(ierr);
/* Now set blocks of values */
for (j=0; j<bs*bs; j++) vals[j] = 0.0;
for (i=0; i<Mbs; i++) {
cols[0] = i*bs; rows[0] = i*bs;
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
/* second, add random blocks */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
cols[0] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
rows[0] = rstart + bs*(PetscInt)(PetscRealPart(rval)*mbs);
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
for (j=0; j<bs*bs; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
vals[j] = rval;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* make A a symmetric matrix: A <- A^T + A */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,one,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatEqual(A, Atrans, &flg);CHKERRQ(ierr);
if (flg) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_SELF,1,"A+A^T is non-symmetric");
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
/* create a SeqSBAIJ matrix sA (= A) */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
if (vid >= 0 && vid < size) {
if (!rank) printf("A: \n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
if (!rank) printf("sA: \n");
ierr = MatView(sA,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test sA==A through MatMult() */
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Error in MatConvert(): A != sA");
/* Test MatIncreaseOverlap() */
ierr = PetscMalloc1(nd,&is1);CHKERRQ(ierr);
ierr = PetscMalloc1(nd,&is2);CHKERRQ(ierr);
for (i=0; i<nd; i++) {
if (!TestAllcols) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
sz = (PetscInt)((0.5+0.2*PetscRealPart(rval))*mbs); /* 0.5*mbs < sz < 0.7*mbs */
for (j=0; j<sz; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
idx[j*bs] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
for (k=1; k<bs; k++) idx[j*bs+k] = idx[j*bs]+k;
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is1+i);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is2+i);CHKERRQ(ierr);
if (rank == vid) {
ierr = PetscPrintf(PETSC_COMM_SELF," [%d] IS sz[%d]: %d\n",rank,i,sz);CHKERRQ(ierr);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
} else { /* Test all rows and colums */
sz = M;
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is1+i);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is2+i);CHKERRQ(ierr);
if (rank == vid) {
PetscBool colflag;
ierr = ISIdentity(is2[i],&colflag);CHKERRQ(ierr);
printf("[%d] is2[%d], colflag %d\n",rank,(int)i,(int)colflag);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
}
}
ierr = PetscLogStageRegister("MatOv_SBAIJ",&stages[0]);CHKERRQ(ierr);
ierr = PetscLogStageRegister("MatOv_BAIJ",&stages[1]);CHKERRQ(ierr);
/* Test MatIncreaseOverlap */
if (TestOverlap) {
ierr = PetscLogStagePush(stages[0]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(sA,nd,is2,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
ierr = PetscLogStagePush(stages[1]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(A,nd,is1,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
if (rank == vid) {
printf("\n[%d] IS from BAIJ:\n",rank);
ierr = ISView(is1[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
printf("\n[%d] IS from SBAIJ:\n",rank);
ierr = ISView(is2[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
for (i=0; i<nd; ++i) {
ierr = ISEqual(is1[i],is2[i],&flg);CHKERRQ(ierr);
if (!flg) {
if (!rank) {
ierr = ISSort(is1[i]);CHKERRQ(ierr);
/* ISView(is1[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
ierr = ISSort(is2[i]);CHKERRQ(ierr);
/* ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
}
SETERRQ1(PETSC_COMM_SELF,1,"i=%D, is1 != is2",i);
}
}
}
/* Test MatCreateSubmatrices */
if (TestSubMat) {
if (test_sorted) {
for (i = 0; i < nd; ++i) {
ierr = ISSort(is1[i]);CHKERRQ(ierr);
}
}
ierr = MatCreateSubMatrices(A,nd,is1,is1,MAT_INITIAL_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatCreateSubMatrices(sA,nd,is1,is1,MAT_INITIAL_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A != sA");
/* Now test MatCreateSubmatrices with MAT_REUSE_MATRIX option */
ierr = MatCreateSubMatrices(A,nd,is1,is1,MAT_REUSE_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatCreateSubMatrices(sA,nd,is1,is1,MAT_REUSE_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatCreateSubmatrices(): A != sA");
ierr = MatDestroySubMatrices(nd,&submatA);CHKERRQ(ierr);
ierr = MatDestroySubMatrices(nd,&submatsA);CHKERRQ(ierr);
}
/* Free allocated memory */
for (i=0; i<nd; ++i) {
ierr = ISDestroy(&is1[i]);CHKERRQ(ierr);
ierr = ISDestroy(&is2[i]);CHKERRQ(ierr);
}
ierr = PetscFree(is1);CHKERRQ(ierr);
ierr = PetscFree(is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = PetscFree(cols);CHKERRQ(ierr);
ierr = PetscFree(vals);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
{
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(((PetscObject)A)->comm,1,"FormTestMatrix: These problems require complex numbers.");
#else
PetscScalar val[5];
PetscErrorCode ierr;
PetscInt i,j,Ii,J,col[5],Istart,Iend;
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
if (type == TEST_1) {
val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-1; col[0] = n-2; col[1] = n-1;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == TEST_2) {
val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
for (i=2; i<n-1; i++) {
col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
ierr = MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);CHKERRQ(ierr);
i = 0;
ierr = MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == TEST_3) {
val[0] = PETSC_i * 2.0;
val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
for (i=1; i<n-3; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
ierr = MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
ierr = MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = n-1; col[0] = n-2; col[1] = n-1;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
ierr = MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == HELMHOLTZ_1) {
/* Problem domain: unit square: (0,1) x (0,1)
Solve Helmholtz equation:
-delta u - sigma1*u + i*sigma2*u = f,
where delta = Laplace operator
Dirichlet b.c.'s on all sides
*/
PetscRandom rctx;
PetscReal h2,sigma1 = 5.0;
PetscScalar sigma2;
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
h2 = 1.0/((n+1)*(n+1));
for (Ii=Istart; Ii<Iend; Ii++) {
*val = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);
*val = 4.0 - sigma1*h2 + sigma2*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
}
else if (type == HELMHOLTZ_2) {
/* Problem domain: unit square: (0,1) x (0,1)
Solve Helmholtz equation:
-delta u - sigma1*u = f,
where delta = Laplace operator
Dirichlet b.c.'s on 3 sides
du/dn = i*alpha*u on (1,y), 0<y<1
*/
PetscReal h2,sigma1 = 200.0;
PetscScalar alpha_h;
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
h2 = 1.0/((n+1)*(n+1));
alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
for (Ii=Istart; Ii<Iend; Ii++) {
*val = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
*val = 4.0 - sigma1*h2;
if (!((Ii+1)%n)) *val += alpha_h;
ierr = MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);CHKERRQ(ierr);
}
}
else SETERRQ(((PetscObject)A)->comm,1,"FormTestMatrix: unknown test matrix type");
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
#endif
return 0;
}
int main(int argc, char** args){
PetscErrorCode err;
PetscViewer fd = NULL;
Mat invL1 = NULL, invU1 = NULL, invL2 = NULL, invU2 = NULL, H12 = NULL, H21 = NULL;
Vec order = NULL, r = NULL; //, or = NULL; //dimension: n: n1 + n2
Vec seeds = NULL;
// Vec r1 = NULL, q1 = NULL, t1_1 = NULL, t1_2 = NULL, t1_3 = NULL, t1_4 = NULL, t1_5 = NULL; // dimension: n1
// Vec r2 = NULL, q2 = NULL, q_tilda = NULL, t2_1 = NULL, t2_2 = NULL, t2_3 = NULL; // dimension: n2
PetscRandom rand;
PetscLogDouble tic, toc, total_time, time;
PetscInt n, i;
PetscMPIInt rank, size;
PetscInt seed;
PetscScalar c, val;
PetscInt QN = 100;
// Initialize PETSC and MPI
err = PetscInitialize(&argc, &args, (char*) 0, help); CHKERRQ(err);
err = MPI_Comm_size(PETSC_COMM_WORLD, &size); CHKERRQ(err);
err = MPI_Comm_rank(PETSC_COMM_WORLD, &rank); CHKERRQ(err);
err = PetscPrintf(PETSC_COMM_WORLD, "mpi size: %d\n", size); CHKERRQ(err);
// Read matrices and an ordering vector
err = PetscPrintf(PETSC_COMM_WORLD, "Read inputs (invL1, invU1, invL2, invU2, H12, H21, order)\n"); CHKERRQ(err);
err = loadMat("./data/invL1.dat", &invL1, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invL1", invL1); CHKERRQ(err);
err = loadMat("./data/invU1.dat", &invU1, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invU1", invU1); CHKERRQ(err);
err = loadMat("./data/invL2.dat", &invL2, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invL2", invL2); CHKERRQ(err);
err = loadMat("./data/invU2.dat", &invU2, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invU2", invU2); CHKERRQ(err);
err = loadMat("./data/H12.dat", &H12, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("H12", H12); CHKERRQ(err);
err = loadMat("./data/H21.dat", &H21, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("H21", H21); CHKERRQ(err);
err = loadVec("./data/order.dat", &order, PETSC_COMM_SELF, &fd); CHKERRQ(err); //all processes must have this vector for ordering the result vector.
err = checkVec("order", order); CHKERRQ(err);
// shift -1 for zero-based index
err = VecShift(order, -1); CHKERRQ(err);
err = VecGetSize(order, &n); CHKERRQ(err);
seed = 5;
c = 0.05;
err = PetscTime(&tic); CHKERRQ(err);
//err = BearQueryMat(seed, c, invL1, invU1, invL2, invU2, H12, H21, order); CHKERRQ(err);
//err = PetscTime(&toc); CHKERRQ(err);
//time = toc - tic;
//err = PetscPrintf(PETSC_COMM_WORLD, "running time: %f sec\n", time); CHKERRQ(err);
///* 100 times querying
err = VecCreateSeq(PETSC_COMM_SELF, QN, &seeds); CHKERRQ(err);
err = VecSetFromOptions(seeds); CHKERRQ(err);
err = PetscRandomCreate(PETSC_COMM_WORLD, &rand); CHKERRQ(err);
err = PetscRandomSetSeed(rand, 100); CHKERRQ(err);
err = PetscRandomSetInterval(rand, (PetscScalar) 0, (PetscScalar) n); CHKERRQ(err);
err = PetscRandomSetFromOptions(rand); CHKERRQ(err);
err = VecSetRandom(seeds, rand); CHKERRQ(err);
err = PetscRandomDestroy(&rand); CHKERRQ(err);
seed = 5; //seed is give by user on one-based index
c = 0.05;
i = 0;
err = VecDuplicate(order, &r); CHKERRQ(err);
for(i = 0; i < QN; i++){
err = VecGetValues(seeds, 1, &i, &val);
seed = (PetscInt) val;
//err = PetscPrintf(PETSC_COMM_SELF, "rank: %d, seed: %d\n", rank, seed);
err = PetscTime(&tic); CHKERRQ(err);
err = BearQuery(seed, c, invL1, invU1, invL2, invU2, H12, H21, order, r); CHKERRQ(err);
err = PetscTime(&toc); CHKERRQ(err);
time = toc - tic;
err = PetscPrintf(PETSC_COMM_WORLD, "running time: %f sec\n", time); CHKERRQ(err);
total_time += time;
}
err = PetscPrintf(PETSC_COMM_WORLD, "average running time: %f sec\n", total_time/QN); CHKERRQ(err);
err = VecDestroy(&r);
/* err = MatGetSize(H12, &n1, &n2); CHKERRQ(err);
n = n1 + n2;
err = PetscPrintf(PETSC_COMM_WORLD, "n1: %d, n2: %d\n", n1, n2); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n, &r); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n1, &q1); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n2, &q2); CHKERRQ(err);
err = VecSet(q1, 0); CHKERRQ(err);
err = VecSet(q2, 0); CHKERRQ(err);
seed = seed - 1; // shift -1 for zero-based index
err = VecGetValues(order, 1, &seed, &val); CHKERRQ(err);
oseed = (PetscInt) val;
err = PetscPrintf(PETSC_COMM_WORLD, "Given seed: %d, Reorered seed: %d (0 ~ n-1)\n", seed, oseed); CHKERRQ(err);
if(oseed < n1){
err = VecSetValues(q1, 1, &oseed, &one, INSERT_VALUES); CHKERRQ(err);
}else{
oseed = oseed - n1;
err = VecSetValues(q2, 1, &oseed, &one, INSERT_VALUES); CHKERRQ(err);
//err = printVecSum(q2);
}
err = VecAssemblyBegin(q1); CHKERRQ(err);
err = VecAssemblyBegin(q2); CHKERRQ(err);
err = VecAssemblyEnd(q1); CHKERRQ(err);
err = VecAssemblyEnd(q2); CHKERRQ(err);
err = VecDuplicate(q1, &r1); CHKERRQ(err);
err = VecDuplicate(q1, &t1_1); CHKERRQ(err);
err = VecDuplicate(q1, &t1_2); CHKERRQ(err);
err = VecDuplicate(q1, &t1_3); CHKERRQ(err);
err = VecDuplicate(q1, &t1_4); CHKERRQ(err);
err = VecDuplicate(q1, &t1_5); CHKERRQ(err);
err = VecDuplicate(q2, &r2); CHKERRQ(err);
err = VecDuplicate(q2, &q_tilda); CHKERRQ(err);
err = VecDuplicate(q2, &t2_1); CHKERRQ(err);
err = VecDuplicate(q2, &t2_2); CHKERRQ(err);
err = VecDuplicate(q2, &t2_3); CHKERRQ(err);
// Start matrix-vec multiplications
err = MatMult(invL1, q1, t1_1); CHKERRQ(err);
err = MatMult(invU1, t1_1, t1_2); CHKERRQ(err);
err = MatMult(H21, t1_2, t2_1); CHKERRQ(err);
err = VecAXPBYPCZ(q_tilda, 1.0, -1.0, 0.0, q2, t2_1); CHKERRQ(err);
err = MatMult(invL2, q_tilda, t2_2); CHKERRQ(err);
err = MatMult(invU2, t2_2, r2); CHKERRQ(err);
err = MatMult(H12, r2, t1_3); CHKERRQ(err);
err = VecAXPBYPCZ(t1_4, 1.0, -1.0, 0.0, q1, t1_3); CHKERRQ(err);
err = MatMult(invL1, t1_4, t1_5); CHKERRQ(err);
err = MatMult(invU1, t1_5, r1); CHKERRQ(err);
//err = printVecSum(r1);
//err = VecView(r2, PETSC_VIEWER_STDOUT_WORLD);
// Concatenate r1 and r2
err = VecMerge(r1, r2, r); CHKERRQ(err);
err = VecScale(r, c); CHKERRQ(err);
//err = VecView(r, PETSC_VIEWER_STDOUT_WORLD);
err = VecDuplicate(r, &or); CHKERRQ(err);
err = VecReorder(r, order, or); CHKERRQ(err);
//err = VecView(or, PETSC_VIEWER_STDOUT_WORLD);*/
// Destory matrices and vectors
err = MatDestroy(&invL1); CHKERRQ(err);
err = MatDestroy(&invU1); CHKERRQ(err);
err = MatDestroy(&invL2); CHKERRQ(err);
err = MatDestroy(&invU2); CHKERRQ(err);
err = MatDestroy(&H12); CHKERRQ(err);
err = MatDestroy(&H21); CHKERRQ(err);
err = VecDestroy(&order); CHKERRQ(err);
err = VecDestroy(&r); CHKERRQ(err);
err = VecDestroy(&seeds); CHKERRQ(err);
//err = VecDestroy(&or); CHKERRQ(err);
/* err = VecDestroy(&r1); CHKERRQ(err);
err = VecDestroy(&q1); CHKERRQ(err);
err = VecDestroy(&t1_1); CHKERRQ(err);
err = VecDestroy(&t1_2); CHKERRQ(err);
err = VecDestroy(&t1_3); CHKERRQ(err);
err = VecDestroy(&t1_4); CHKERRQ(err);
err = VecDestroy(&t1_5); CHKERRQ(err);
err = VecDestroy(&r2); CHKERRQ(err);
err = VecDestroy(&q2); CHKERRQ(err);
err = VecDestroy(&q_tilda); CHKERRQ(err);
err = VecDestroy(&t2_1); CHKERRQ(err);
err = VecDestroy(&t2_2); CHKERRQ(err);
err = VecDestroy(&t2_3); CHKERRQ(err);*/
// Finalize
err = PetscFinalize(); CHKERRQ(err);
return 0;
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=50,N1=20,N=N0*N1,DIM;
PetscRandom rdm;
PetscScalar a;
PetscReal enorm;
Vec x,y,z;
PetscBool view=PETSC_FALSE,use_interface=PETSC_TRUE;
ierr = PetscInitialize(&argc,&args,(char*)0,help);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex numbers");
#endif
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "FFTW Options", "ex143");CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the vectors", "ex143", view, &view, NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-use_FFTW_interface", "Use PETSc-FFTW interface", "ex143",use_interface, &use_interface, NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-use_FFTW_interface",&use_interface,NULL);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
if (!use_interface) {
/* Use mpi FFTW without PETSc-FFTW interface, 2D case only */
/*---------------------------------------------------------*/
fftw_plan fplan,bplan;
fftw_complex *data_in,*data_out,*data_out2;
ptrdiff_t alloc_local,local_n0,local_0_start;
DIM = 2;
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Use FFTW without PETSc-FFTW interface, DIM %D\n",DIM);CHKERRQ(ierr);
}
fftw_mpi_init();
N = N0*N1;
alloc_local = fftw_mpi_local_size_2d(N0,N1,PETSC_COMM_WORLD,&local_n0,&local_0_start);
data_in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out2 = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_in,&x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real Space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out,&y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out2,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
fplan = fftw_mpi_plan_dft_2d(N0,N1,data_in,data_out,PETSC_COMM_WORLD,FFTW_FORWARD,FFTW_ESTIMATE);
bplan = fftw_mpi_plan_dft_2d(N0,N1,data_out,data_out2,PETSC_COMM_WORLD,FFTW_BACKWARD,FFTW_ESTIMATE);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
if (view) {ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(fplan);
if (view) {ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(bplan);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view) {ierr = VecView(z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11 && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %g\n",(double)enorm);CHKERRQ(ierr);
}
/* Free spaces */
fftw_destroy_plan(fplan);
fftw_destroy_plan(bplan);
fftw_free(data_in); ierr = VecDestroy(&x);CHKERRQ(ierr);
fftw_free(data_out); ierr = VecDestroy(&y);CHKERRQ(ierr);
fftw_free(data_out2);ierr = VecDestroy(&z);CHKERRQ(ierr);
} else {
/* Use PETSc-FFTW interface */
/*-------------------------------------------*/
PetscInt i,*dim,k;
Mat A;
N=1;
for (i=1; i<5; i++) {
DIM = i;
ierr = PetscMalloc1(i,&dim);CHKERRQ(ierr);
for (k=0; k<i; k++) {
dim[k]=30;
}
N *= dim[i-1];
/* Create FFTW object */
if (!rank) printf("Use PETSc-FFTW interface...%d-DIM: %d\n",(int)DIM,(int)N);
ierr = MatCreateFFT(PETSC_COMM_WORLD,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
/* Create vectors that are compatible with parallel layout of A - must call MatCreateVecs()! */
ierr = MatCreateVecsFFTW(A,&x,&y,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* Set values of space vector x */
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
if (view) {ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* Apply FFTW_FORWARD and FFTW_BACKWARD */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
if (view) {ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view) {ierr = VecView(z,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-9 && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFree(dim);CHKERRQ(ierr);
}
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Vec x,y,b;
Mat A; /* linear system matrix */
Mat sA,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,col[3],block, row,Ii,J,n1,lvl;
PetscErrorCode ierr;
PetscMPIInt size;
PetscReal norm2,tol=1.e-10,err[10];
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm,cperm;
PetscRandom rdm;
PetscBool reorder = PETSC_FALSE,displ = PETSC_FALSE;
MatFactorInfo factinfo;
PetscBool equal;
PetscBool TestAIJ = PETSC_FALSE,TestBAIJ = PETSC_TRUE;
PetscInt TestShift=0;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-reorder",&reorder,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-testaij",&TestAIJ,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-testShift",&TestShift,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-displ",&displ,NULL);CHKERRQ(ierr);
n = mbs*bs;
if (TestAIJ) { /* A is in aij format */
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestBAIJ = PETSC_FALSE;
} else { /* A is in baij format */
ierr =MatCreateSeqBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestAIJ = PETSC_FALSE;
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
if (TestShift) {
/* set diagonals in the 0-th block as 0 for testing shift numerical factor */
for (i=0; i<bs; i++) {
row = i; col[0] = i; value[0] = 0.0;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatConvert */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,20,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A != sA");
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Vectors */
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatReordering() - not work on sbaij matrix */
if (reorder) {
ierr = MatGetOrdering(A,MATORDERINGRCM,&perm,&cperm);CHKERRQ(ierr);
} else {
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&cperm);CHKERRQ(ierr);
}
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
/* initialize factinfo */
ierr = MatFactorInfoInitialize(&factinfo);CHKERRQ(ierr);
if (TestShift == 1) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_NONZERO;
factinfo.shiftamount = 0.1;
} else if (TestShift == 2) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE;
}
/* Test MatCholeskyFactor(), MatICCFactor() */
/*------------------------------------------*/
/* Test aij matrix A */
if (TestAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"AIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test baij matrix A */
if (TestBAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"BAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test sbaij matrix sA */
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"SBAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sA,&factinfo);CHKERRQ(ierr);
if (lvl==0 && bs==1) { /* Test inplace ICC(0) for sbaij sA - does not work for new datastructure */
/*
Mat B;
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
ierr = MatICCFactor(B,perm,&factinfo);CHKERRQ(ierr);
ierr = MatEqual(sC,B,&equal);CHKERRQ(ierr);
if (!equal) {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"in-place Cholesky factor != out-place Cholesky factor");
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
*/
}
ierr = MatMult(sA,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
/* Test MatSolves() */
if (bs == 1) {
Vecs xx,bb;
ierr = VecsCreateSeq(PETSC_COMM_SELF,n,4,&xx);CHKERRQ(ierr);
ierr = VecsDuplicate(xx,&bb);CHKERRQ(ierr);
ierr = MatSolves(sC,bb,xx);CHKERRQ(ierr);
ierr = VecsDestroy(xx);CHKERRQ(ierr);
ierr = VecsDestroy(bb);CHKERRQ(ierr);
}
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i] -= norm2;
if (err[i] > tol) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_USER," level: %d, err: %g\n", lvl,(double)err[i]);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
DM da; /* distributed array */
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscRandom rctx; /* random number generator context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,its;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE;
PetscLogStage stage;
DMDALocalInfo info;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/*
Create distributed array to handle parallel distribution.
The problem size will default to 8 by 7, but this can be
changed using -da_grid_x M -da_grid_y N
*/
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix preallocated according to the DMDA, format AIJ by default.
To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
*/
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Rows and columns are specified by the stencil
- Entries are normalized for a domain [0,1]x[0,1]
*/
ierr = PetscLogStageRegister("Assembly", &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscReal hx = 1./info.mx,hy = 1./info.my;
MatStencil row = {0},col[5] = {{0}};
PetscScalar v[5];
PetscInt ncols = 0;
row.j = j; row.i = i;
col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
/* boundaries */
if (i>0) {col[ncols].j = j; col[ncols].i = i-1; v[ncols++] = -hy/hx;}
if (i<info.mx-1) {col[ncols].j = j; col[ncols].i = i+1; v[ncols++] = -hy/hx;}
if (j>0) {col[ncols].j = j-1; col[ncols].i = i; v[ncols++] = -hx/hy;}
if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i; v[ncols++] = -hx/hy;}
ierr = MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
/*
Create parallel vectors compatible with the DMDA.
*/
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
By default we use an exact solution of a vector with all
elements of 1.0; Alternatively, using the runtime option
-random_sol forms a solution vector with random components.
*/
ierr = PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,1.);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
These options will override those specified above as long as
KSPSetFromOptions() is called _after_ any other customization
routines.
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecAXPY(x,-1.,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single
print statement from all processes that share a communicator.
An alternative is PetscFPrintf(), which prints to a file.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_summary).
*/
ierr = PetscFinalize();
return 0;
}
/*@
MFNSetFromOptions - Sets MFN options from the options database.
This routine must be called before MFNSetUp() if the user is to be
allowed to set the solver type.
Collective on MFN
Input Parameters:
. mfn - the matrix function context
Notes:
To see all options, run your program with the -help option.
Level: beginner
@*/
PetscErrorCode MFNSetFromOptions(MFN mfn)
{
PetscErrorCode ierr;
char type[256],monfilename[PETSC_MAX_PATH_LEN];
PetscBool flg,flg1,flg2;
PetscReal r;
PetscInt i;
PetscViewer monviewer;
PetscFunctionBegin;
PetscValidHeaderSpecific(mfn,MFN_CLASSID,1);
if (!MFNRegisterAllCalled) { ierr = MFNRegisterAll();CHKERRQ(ierr); }
ierr = PetscObjectOptionsBegin((PetscObject)mfn);CHKERRQ(ierr);
ierr = PetscOptionsFList("-mfn_type","Matrix Function method","MFNSetType",MFNList,(char*)(((PetscObject)mfn)->type_name?((PetscObject)mfn)->type_name:MFNKRYLOV),type,256,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MFNSetType(mfn,type);CHKERRQ(ierr);
}
/*
Set the type if it was never set.
*/
if (!((PetscObject)mfn)->type_name) {
ierr = MFNSetType(mfn,MFNKRYLOV);CHKERRQ(ierr);
}
ierr = PetscOptionsBoolGroupBegin("-mfn_exp","matrix exponential","MFNSetFunction",&flg);CHKERRQ(ierr);
if (flg) {
ierr = MFNSetFunction(mfn,SLEPC_FUNCTION_EXP);CHKERRQ(ierr);
}
ierr = PetscOptionsScalar("-mfn_scale","Scale factor","MFNSetScaleFactor",mfn->sfactor,&mfn->sfactor,NULL);CHKERRQ(ierr);
i = mfn->max_it;
ierr = PetscOptionsInt("-mfn_max_it","Maximum number of iterations","MFNSetTolerances",mfn->max_it,&i,&flg1);CHKERRQ(ierr);
r = mfn->tol;
ierr = PetscOptionsReal("-mfn_tol","Tolerance","MFNSetTolerances",mfn->tol==PETSC_DEFAULT?SLEPC_DEFAULT_TOL:mfn->tol,&r,&flg2);CHKERRQ(ierr);
if (flg1 || flg2) {
ierr = MFNSetTolerances(mfn,r,i);CHKERRQ(ierr);
}
ierr = PetscOptionsInt("-mfn_ncv","Number of basis vectors","MFNSetDimensions",mfn->ncv,&i,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MFNSetDimensions(mfn,i);CHKERRQ(ierr);
}
ierr = PetscOptionsBool("-mfn_error_if_not_converged","Generate error if solver does not converge","MFNSetErrorIfNotConverged",mfn->errorifnotconverged,&mfn->errorifnotconverged,NULL);CHKERRQ(ierr);
/* -----------------------------------------------------------------------*/
/*
Cancels all monitors hardwired into code before call to MFNSetFromOptions()
*/
flg = PETSC_FALSE;
ierr = PetscOptionsBool("-mfn_monitor_cancel","Remove any hardwired monitor routines","MFNMonitorCancel",flg,&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = MFNMonitorCancel(mfn);CHKERRQ(ierr);
}
/*
Prints error estimate at each iteration
*/
ierr = PetscOptionsString("-mfn_monitor","Monitor error estimate","MFNMonitorSet","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (flg) {
ierr = PetscViewerASCIIOpen(PetscObjectComm((PetscObject)mfn),monfilename,&monviewer);CHKERRQ(ierr);
ierr = MFNMonitorSet(mfn,MFNMonitorDefault,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);CHKERRQ(ierr);
}
flg = PETSC_FALSE;
ierr = PetscOptionsBool("-mfn_monitor_lg","Monitor error estimate graphically","MFNMonitorSet",flg,&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = MFNMonitorSet(mfn,MFNMonitorLG,NULL,NULL);CHKERRQ(ierr);
}
/* -----------------------------------------------------------------------*/
ierr = PetscOptionsName("-mfn_view","Print detailed information on solver used","MFNView",0);CHKERRQ(ierr);
if (mfn->ops->setfromoptions) {
ierr = (*mfn->ops->setfromoptions)(mfn);CHKERRQ(ierr);
}
ierr = PetscObjectProcessOptionsHandlers((PetscObject)mfn);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
if (!mfn->V) { ierr = MFNGetBV(mfn,&mfn->V);CHKERRQ(ierr); }
ierr = BVSetFromOptions(mfn->V);CHKERRQ(ierr);
if (!mfn->ds) { ierr = MFNGetDS(mfn,&mfn->ds);CHKERRQ(ierr); }
ierr = DSSetFromOptions(mfn->ds);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(mfn->rand);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
